Comptes Rendus
no. 10
Algebraic geometry
Birational geometry of the moduli space of pure sheaves on quadric surface
[Géométrie birationnelle de l'espace moduli des faisceaux purs sur une surface quadrique]

Présenté par : Claire Voisin

Kiryong Chung1 ; Han-Bom Moon2
1 Department of Mathematics Education, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea
2 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States
Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1082-1088.

Dans cette note, nous étudions la géométrie birationnelle de l'espace des modules des faisceaux stables sur une quadrique, de polynôme de Hilbert 5m+1 et de classes de Chern (2,3). Pour cela, nous donnons une application birationnelle entre l'espace des modules et un fibré projectif au dessus d'une grassmanienne, qui est une composition d'éclatements et de contractions lisses.

We study birational geometry of the moduli space of stable sheaves on a quadric surface with Hilbert polynomial 5m+1 and c1=(2,3). We describe a birational map between the moduli space and a projective bundle over a Grassmannian as a composition of smooth blow-ups/downs.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.09.005
Kiryong Chung 1 ; Han-Bom Moon 2

1 Department of Mathematics Education, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea
2 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States 
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Kiryong Chung; Han-Bom Moon. Birational geometry of the moduli space of pure sheaves on quadric surface. Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1082-1088. doi : 10.1016/j.crma.2017.09.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.005/

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[10] J. Kollár; S. Mori Birational Geometry of Algebraic Varieties, Camb. Tracts Math., vol. 134, Cambridge University Press, Cambridge, 1998

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[13] M. Maican Moduli of sheaves supported on curves of genus two in a quadric surface, 2016 | arXiv

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